|Nothing quite like seeing an airshow from above the planes|
Saturday, September 29, 2012
Consistency and Completeness
To all my regular readers (ha, as if I have regular readers!) sorry I haven't written in such a long time. I've been busy going overseas to a combat zone.
Anyways, I've been reading Gödel, Escher, Bach: An Eternal Golden Braid and the author brings up an interesting concept. Can one actually conceive of a universe that doesn't follow logical rules? In that regard one might use the copout argument that just writing or saying the words means that one can conceive of it. But that's a silly argument, and doesn't really count. That's like being able to read Korean script but having no knowledge of what's being said. Just being able to say the words doesn't mean that it's actually conceivable.
But, it is conceivable? Think about sci-fi movies and such... or a world that doesn't have mathematical consistency. Could, even in a movie, there be a world where 1 + 1 = 3? I'm not talking about the words 'one,' 'plus,' 'equals,' and 'three.' Even in this world there are a variety of ways to express the number '1' but could there exist a world where having two of something couldn't exist? In the movies it is easy (or is it?) to blur the lines between conceivable and inconceivable.
The book often references "zen" and that zen readily accepts contradictions. It seems like cheating to me... like saying 1+1=2 and 1+1=3, and just accepting both as being completely correct. It's like throwing out Aristotle's laws of non-contradiction. The same thing, at the same time cannot be two opposite things! According to Aristotle without these distinctions we cannot know anything, to which zen would probably responds "yes, we cannot know anything." Accepting contradiction is not a way of dealing with it, it's a way of ignoring it. I would guess that zen would eventually draw a line somewhere and stick to some standard. Maybe not, but even if one ignores a fact or a non-fact does that make it any more of a fact or non-fact?